A Class of Polynomial Modules over Map Lie Algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-17 DOI:10.1007/s40304-023-00356-4

Hongjia Chen, Han Dai, Xingpeng Liu

引用次数: 0

Abstract

For any finitely generated unital commutative associative algebra \(\mathcal {R}\) over \(\mathbb {C}\) and any complex finite-dimensional simple Lie algebra \(\mathfrak {g}\) with a fixed Cartan subalgebra \(\mathfrak {h}\), we classify all \(\mathfrak {g}\otimes \mathcal {R}\)-modules on \(U(\mathfrak {h})\) such that \(\mathfrak {h}\) as a subalgebra of \(\mathfrak {g}\otimes \mathcal {R}\), acts on \(U(\mathfrak {h})\) by the multiplication. We construct these modules explicitly and study their module structures.

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映射李代数上的一类多项式模块

对于任何在\(\mathbb {C}\)上有限生成的单元交换关联代数\(\mathcal {R}\)和任何复杂的有限维简单李代数\(\mathfrak {g}\)，都有一个固定的笛卡尔子代数\(\mathfrak {h}\)、我们将所有关于\(U(\mathfrak {h})\的\(\mathfrak {g}\otimes\mathcal{R}\)模块分类，使得\(\mathfrak {h}\)作为\(\mathfrak {g}\otimes\mathcal{R}\)的子代数，通过乘法作用于\(U(\mathfrak {h})\。我们明确地构造了这些模块，并研究了它们的模块结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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